A prism has a right triangle as its base with a hypotenuse that measures 15 meters and legs that measure 9 meters and 12 meters. What is the surface area of this prism if the height of the prism is 11 meters?
The three rectangular faces are
11x15, 11x12 and 11x9 m^2
Add their areas.
Then add the areas of the two ends, which (combined) is 9 x 12 m^2
To find the surface area of the prism, we need to calculate the area of each face and then sum them up.
The base of the prism is a right triangle with legs measuring 9 meters and 12 meters. The area of a triangle can be calculated using the formula: 0.5 * base * height.
In this case, the base is 9 meters and the height is 12 meters, so the area of the base is: 0.5 * 9 * 12 = 54 square meters.
The prism has three rectangular faces. Two of these faces are congruent and have dimensions 9 meters by 11 meters. The area of each of these faces is: length * width = 9 * 11 = 99 square meters.
The third rectangular face has dimensions 12 meters by 11 meters. The area of this face is: length * width = 12 * 11 = 132 square meters.
Now, sum up the areas of all the faces: 54 + 99 + 99 + 132 = 384 square meters.
Therefore, the surface area of this prism is 384 square meters.